Geodesic
A boundary value problem for a differential equation of second order
Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 373-384 
B. V. Verbitskii. A boundary value problem for a differential equation of second order. Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 373-384. http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a5/
@article{MZM_1973_13_3_a5,
     author = {B. V. Verbitskii},
     title = {A~boundary value problem for a~differential equation of second order},
     journal = {Matemati\v{c}eskie zametki},
     pages = {373--384},
     year = {1973},
     volume = {13},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a5/}
}
TY  - JOUR
AU  - B. V. Verbitskii
TI  - A boundary value problem for a differential equation of second order
JO  - Matematičeskie zametki
PY  - 1973
SP  - 373
EP  - 384
VL  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a5/
LA  - ru
ID  - MZM_1973_13_3_a5
ER  - 
%0 Journal Article
%A B. V. Verbitskii
%T A boundary value problem for a differential equation of second order
%J Matematičeskie zametki
%D 1973
%P 373-384
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a5/
%G ru
%F MZM_1973_13_3_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

We find the spectrum and prove a theorem on the expansion of an arbitrary function satisfying certain smoothness conditions in terms of the root functions of a boundary value problem of the type \begin{gather*} -y''+q(x)+\frac a{x^2}y=\lambda y,\quad y(0)=0, \\ M(\lambda)y(a)+N(\lambda)y(b)=0, \end{gather*} where $0, $a\ge0$, $M(\lambda)$ and $N(\lambda)$ are polynomials with complex coefficients, and $q(x)$ is a sufficiently smooth complex-valued function.